The Lancelet (1975) reported on the relationship between the ages of a number of children who had high levels of lead absorption and a measure of wrist flexor and extensor muscle function for these children. The measure involved the number of taps with a stylus on a single metal plate during a 10-second period. Representative data were as follows, with X = age in months and Y = taps/10sec.: X 73 84 98 112 116 132 150 160 164 180 Y 35 40 50 42 46 41 52 52 51 66 (a) Calculate the least squares regression line of Y on X. (b) What would be your estimate of expected change in the measure of muscle function for i. a one-month old, and ii. a one-year old in age? (c) Estimate the true average measure of muscle function for a 10-year old in the population sample. Then set up a 95% confidence interval. (d) Test the null hypothesis that the slope of the regression line is zero, using a 5% level of significance. (e) Construct the 95% confidence interval for the slope of the regression line.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The Lancelet (1975) reported on the relationship between the ages of a number of children who had high levels of lead absorption and a measure of wrist flexor and extensor muscle
X 73 84 98 112 116 132 150 160 164 180
Y 35 40 50 42 46 41 52 52 51 66
(a) Calculate the least squares regression line of Y on X. (b) What would be your estimate of expected change in the measure of muscle function for i. a one-month old, and ii. a one-year old in age? (c) Estimate the true average measure of muscle function for a 10-year old in the population sample. Then set up a 95% confidence interval. (d) Test the null hypothesis that the slope of the regression line is zero, using a 5% level of significance. (e) Construct the 95% confidence interval for the slope of the regression line.
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